Great story. It highlighted my thoughts on the Aang/Katara pairing. The Aang/Azula pairing is new for me, but I admit that I am beginning to enjoy it wholeheartedly.
The story itself seemed brief at first, but now I realize that it is, in fact, better this way. Very well written.

Personally, I have always shipped Aang/Azula, and for reasons (dare I say it) similar to yours - though in far, far simpler, far less elegant terms, simply blunt thoughts with no depth, no shine. Okay, I've never even thought of Toph/Aang, but the Aang/Katara pairing I felt was simply too tame, too set, too calm. She's just the one who's there, she's the soft, quiet one...I felt it lacked that spark to set it alight. Though I'll admit that I'd never really thought it out as you have, never seen all those facets of it as you have. As for Aang/Azula, my thought was simply that they were right together. When they fought, they fought so perfectly, two halves of the same whole. I never would have been able to say it like this, nor anything nearly like this, of course.
Of course, I have always been one to go for the 'wrong' pairings, those between enemies. Thus Aang/Azula.
Anyway, great fic! I loved it.
Namarie
Morgaur Melkorian